No abstract

Subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest. Its goal is to determine the heterogeneity of the treatment effect across subpopulations. In this paper, we adapt the idea of recursive partitioning and introduce an interaction tree (IT) procedure to conduct subgroup analysis. The IT procedure automatically facilitates a number of objectively defined subgroups, in some of which the treatment effect is found prominent while in others the treatment has a negligible or even negative effect. The standard CART (Breiman et al., 1984) methodology is inherited to construct the tree structure. Also, in order to extract factors that contribute to the heterogeneity of the treatment effect, variable importance measure is made available via random forests of the interaction trees. Both simulated experiments and analysis of census wage data are presented for illustration.

The penalised least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method. It not only automatically and consistently selects the important variables, but also produces estimators which are as efficient as the oracle estimator. However, these attractive features depend on appropriately choosing the tuning parameter. We show that the commonly used the generalised crossvalidation cannot select the tuning parameter satisfactorily, with a nonignorable overfitting effect in the resulting model. In addition, we propose a bic tuning parameter selector, which is shown to be able to identify the true model consistently. Simulation studies are presented to support theoretical findings, and an empirical example is given to illustrate its use in the Female Labor Supply data.

No abstract